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A293896 Number of proper divisors of n of the form 3k+2.

%I A293896 #17 Nov 25 2023 08:03:59
%S A293896 0,0,0,1,0,1,0,1,0,2,0,1,0,1,1,2,0,1,0,2,0,2,0,2,1,1,0,2,0,2,0,2,1,2,
%T A293896 1,1,0,1,0,4,0,2,0,2,1,2,0,2,0,2,1,2,0,1,2,3,0,2,0,3,0,1,0,3,1,2,0,2,
%U A293896 1,4,0,2,0,1,1,2,1,2,0,4,0,2,0,2,2,1,1,4,0,2,0,2,0,2,1,3,0,2,1,4,0,2,0,3,2
%N A293896 Number of proper divisors of n of the form 3k+2.
%H A293896 Antti Karttunen, <a href="/A293896/b293896.txt">Table of n, a(n) for n = 1..20000</a>
%H A293896 R. A. Smith and M. V. Subbarao, <a href="https://doi.org/10.4153/CMB-1981-005-3">The average number of divisors in an arithmetic progression</a>, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.
%F A293896 a(n) = A001822(n) - [n == 2 (mod 3)].
%F A293896 G.f.: Sum_{k>=1} x^(6*k-2) / (1 - x^(3*k-1)). - _Ilya Gutkovskiy_, Apr 14 2021
%F A293896 Sum_{k=1..n} a(k) = n*log(n)/3 + c*n + O(n^(1/3)*log(n)), where c = gamma(2,3) - (2 - gamma)/3 = A256843 - (2 - A001620)/3 = -0.401054... (Smith and Subbarao, 1981). - _Amiram Eldar_, Nov 25 2023
%t A293896 Table[DivisorSum[n, 1 &, And[Mod[#, 3] == 2, # != n] &], {n, 105}] (* _Michael De Vlieger_, Nov 08 2017 *)
%o A293896 (PARI) A293896(n) = sumdiv(n,d,(d<n)*(2==(d%3)));
%Y A293896 Cf. A001620, A001822, A256843, A293895, A293898, A293899.
%K A293896 nonn,easy
%O A293896 1,10
%A A293896 _Antti Karttunen_, Nov 06 2017